Replica Analysis of the Linear Model with Markov or Hidden Markov Signal Priors
This paper estimates free energy, average mutual information, and minimum mean square error (MMSE) of a linear model under two assumptions: (1) the source is generated by a Markov chain, (2) the source is generated via a hidden Markov model. Our estimates are based on the replica method in statistical physics. We show that under the posterior mean estimator, the linear model with Markov sources or hidden Markov sources is decoupled into single-input AWGN channels with state information available at both encoder and decoder where the state distribution follows the left Perron-Frobenius eigenvector with unit Manhattan norm of the stochastic matrix of Markov chains. Numerical results show that the free energies and MSEs obtained via the replica method are closely approximate to their counterparts achieved by the Metropolis-Hastings algorithm or some well-known approximate message passing algorithms in the research literature.
Code (0)
등록된 구현이 없습니다.
Tasks
DecoderSimilar Papers 제목 키워드 기반
The Restless Hidden Markov Bandit with Linear Rewards and Side Information
In this paper we present a model for the hidden Markovian bandit problem with linear rewards. As opposed to current work on Markovian bandits, we do not assume that the state is known to the decision maker before making …
Generalization of Auto-Regressive Hidden Markov Models to Non-Linear Dynamics and Unit Quaternion Observation Space
Latent variable models are widely used to perform unsupervised segmentation of time series in different context such as robotics, speech recognition, and economics. One of the most widely used latent variable model is th…
speech-recognitionSpeech RecognitionTime SeriesTime Series AnalysisDRL-STAF: A Deep Reinforcement Learning Framework for State-Aware Forecasting of Complex Multivariate Hidden Markov Processes
Forecasting multivariate hidden Markov processes is challenging due to nonlinear and nonstationary observations, latent state transitions, and cross-sequence dependencies. While deep learning methods achieve strong predi…
Reinforcement LearningComparative Analysis of the Hidden Markov Model and LSTM: A Simulative Approach
Time series and sequential data have gained significant attention recently since many real-world processes in various domains such as finance, education, biology, and engineering can be modeled as time series. Although m…
Time SeriesTime Series AnalysisA Linear-Time Particle Gibbs Sampler for Infinite Hidden Markov Models
Infinite Hidden Markov Models (iHMM's) are an attractive, nonparametric generalization of the classical Hidden Markov Model which can automatically infer the number of hidden states in the system. However, due to the inf…